I have a camera that uses a 9-volt battery, or has an AC adapter if I want to plug it in. The battery life is approximately 1.5 hours per 9-volt.

If I connect three or four 9-volt batteries in parallel, so as not to increase voltage output, would I theoretically achieve three or four times the battery life? I would like to get approximately 8 hours of run time...

Would the amperage be changed by a parallel connection? I do not want to burn up my camera!

I just found this...
"When batteries are connected in parallel, they will not share current exactly. If one supplies a slightly higher current, then it will get warmer. As it gets warmer, it will become more efficient, and it will start to supply even more of the current. Hence there is the possibility that it will end up supplying most of the current while the other sits there getting charged up! A solution to this is to insert small value resistors in series with each battery before paralleling them up."

So... it looks as if connecting some 9-volt batteries in parallel may not provide any benefit. I really wanted to make the camera run for around 8 or 9 hours without having to run electricity for the AC adapter!

You mean this kind of 9V battery?
They are cheap so I don´t see any problem getting a few fresh ones and trying it out. You only have to be sure to change them all at once for completely new ones, or you will end up with the fuller ones trying to recharge the dead one.

If the flat 6-AA holder is the wrong shape for the space available, you could get three 2-AA battery holders (or two 3-battery holders) from someplace like Radio Shack or an online vendor, and wire them in series.

Generally putting batteries in parallel is not a great idea. New non-rechargeable batteries will most likely be OK, but never try this with rechargeable types which could be in different states of charge. That can lead to big currents circulating, with the possibility of burned out wiring and batteries failing or even bursting.